Sin[omegat±90°] appears after the derivative or integration of Sin[omegat], so for
the inductor and capacitance connected to the sine wave, the waveform is ahead
of and lag when the horizontal coordinate is met, it's not easy to understand
from the static function diagram. It's better to make animations.
The following figure shows the inductor. Red indicates the voltage and blue indicates the current. If an ideal DC voltmeter and DC ammeter are connected, the voltage changes ahead of the current, and the current changes lag behind the voltage. As time increases, the vertical axis and time origin move to the left along with the waveform.
If you draw the waveform to the right of the vector graph, it's the following animation, but the waveform to the right of the abscissa is the waveform that existed in the past, pointing to the past, and it's -omega. Although the waveform is reversed, the voltage changes ahead of the current, and the current changes lag behind the voltage. The origin of time moves to the right with the waveform. The vertical axis of the function graph does not intersect with the horizontal axis. The time represented by the intersection point increases. If you do not pay attention, the judgment of the lead-delay is easy to be wrong.
The voltage is described in different colors: blue > yellow > red. Different thicknesses and arrows are used to describe the magnitude and direction of the current. In addition, the effect of charging the inductor and capacitor is also made. When the current is the maximum, the magnetic field of the inductor is the largest, and the electric field of the capacitor is the smallest.
However, the animation of the pointer table is more intuitive when explaining the concept of lead-lag.
The total voltage is not shown, because the total voltage may be ahead of the total current, may lag behind the total current, or maybe in the same phase. When the two are in the same phase, they are resonant.
This has been done before, and the component is marked on the right with the reference direction of the voltage and current. Different colors are used to describe the voltage. Blue > yellow > red. Different thicknesses and arrows are used to describe the magnitude and direction of the current. In addition, the effect of charging the inductor and capacitor is also made. When the current is the maximum, the magnetic field of the inductor is the largest, and the electric field of the capacitor is the smallest.
However, the animation of the pointer, table is more intuitive when explaining the concept of lead - lag.
